Pneumonia carries the same silent p as pneumatic, from the same Greek cluster pn-, which English cannot pronounce at the start of a word and so does not. Behind it is Greek pneumōn, "lung," which is itself related to pneuma, "breath, wind" — the lung being, reasonably enough, named as the breath-organ.
English took the word about 1600 from Modern Latin, which had it from Greek pneumonia, "inflammation of the lungs." That is a specific medical distinction: pneumonia affects the lung tissue itself, as opposed to the bronchial tubes or the membrane around the lungs, which have their own names. Greek medical vocabulary reached English almost entirely through Latin and almost entirely after 1500, which is why so much of the anatomy in an English dictionary is spelled in ways English pronunciation cannot honour.
pneumonia (n.) "inflammation of the tissues of the lungs" (as distinct from the bronchial tubes or the serous covering of the lungs), c. 1600, from Modern Latin, from Greek pneumonia "inflammation of the lungs," from pneumōn "lung" (see pneumo- ). also from c. 1600
pneumonia came in through Greek, and its spelling follows that family's conventions.
How that family writes these sounds
| a bare /n/, /t/, /s/, /z/ at the start | put the silent letter back on the front: pn-, pt-, ps-, mn-, x-pneumonia, pterodactyl, psalm, mnemonic, xylophone |
What gives it away on the page
| ps-, pn-, pt-, mn-, x- | Initial clusters English can't actually pronounce, so it silences the first letter.psalm, pneumonia, pterodactyl, mnemonic, xylophone |
Placing it without the spelling
| science, medicine, technical coinage | Greekphotograph, chemistry, system, pneumonia |
| a medical or technical word starting with a bare /n/, /t/, /s/, or /z/ | Greek — the letter you can't hear comes firstpneumonia, pterodactyl, psalm, xylophone |